A Green Proof of Fatou’s Theorem
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This paper is an exposition of some applications of Stochastic Processes to boundary behavior problems for harmonic functions. As an illustration, we give a proof of Fatou’s theorem in simply connected plane domains which is probabilistic and does not use the Riemann mapping theorem. The paper closes with some remarks on further related work and open questions.
AMS Subject Classification31A20 60J45
KeywordsStochastic methods in potential theory Fatou’s theorem Boundary behaviour of harmonic functions
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